Gravity provides the centripetal force

Every orbit question in this topic opens with the same sentence, so bank it: 'The gravitational force provides the centripetal force required for circular motion.' Then write the equation. Two marks before you have thought about the actual question.

Pick the right right-hand side for what you are given. Use mv²/r for speed, mrω² for angular velocity, and m(4π²r/T²) for period. They are the same equation wearing different clothes; converting later wastes time.

The conceptual point examiners chase: centripetal force is a ROLE, not a new kind of force. On a free-body diagram for a satellite you draw ONE arrow, gravity, pointing at the Earth's centre. Adding a separate centripetal arrow, or a centrifugal one, is an automatic loss.

Since the force points at the centre and the velocity is tangential, they are perpendicular. So gravity does NO work on a circular orbit, the speed is constant, and the satellite stays on a single equipotential. Very neat, and it answers a lot of explain questions in one line.

The satellite's own mass m appears on both sides and cancels every time. That is why orbital speed, angular velocity and period depend only on M and r, never on the satellite. Get in the habit of cancelling it explicitly so the marker can see you knew.

The same equation run backwards gives you the mass of the central body. Measure r and T for a moon, and M = 4π²r³/GT². That is literally how the Earth's mass was first found.